<p>"[...]overwhelming majority of Yale admits never apply to Harvard, and vice versa."</p>
<p>that can't possibly be true.</p>
<p>A majority, perhaps, but not an "overwhelming majority" - parsing the quote very carefully. </p>
<p>A "majority" of Yale admits means a little over 900; I'd estimate that roughly 6-700 Yale admits also applied to Harvard, that half were admitted, and that the "overwhelming majority" of <em>this</em> number opted for Harvard.</p>
<p>If Yale took the same fraction of the common admits that it currently loses to Harvard, the overall yield rates would be similar at the two schools.</p>
<p>Your math is overwhelmingly incorrect.</p>